Problem: What's the first wrong statement in the proof below that $ \triangle ABC \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{BD} \cong \overline{BC}$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ $ \angle CEF \cong \angle BAC$ $, \ $ and $\ $ $ \angle ECF \cong \angle ACB$ Proof $ \triangle ABC \cong \triangle EBD$ because SAS $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \angle CEF \cong \angle BCE$ because alternate interior angles are equal $ \overline{AF} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle EFC \cong \triangle ABC$ because AAS $ \triangle ABC \cong \triangle EBC$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{BE} \cong \overline{AF}$ is the first wrong statement.